Birational rigidity of certain classes of higher-dimensional Fano varieties
Lead Research Organisation:
University of Liverpool
Department Name: Mathematical Sciences
Abstract
The aim of the project is to study birational geometry of certain classes of higher-dimensional Fano varieties and prove their birational rigidity, including a description of their groups of birational self-maps. The work is based on the techniques of the method of maximal singularities: the Noether-Fano type inequalities, counting multiplicities and inversion of adjunction. It is planned to put a special emphasis on singular varieties that so far were not studied from the viewpoint of their birational (super)rigidity, showing their factoriality and characterising their singularities in order to obtain effective bounds for the co-dimension of the complement to the set of birationally rigid varieties.
Organisations
People |
ORCID iD |
| Aleksandr Pukhlikov (Primary Supervisor) | |
| Dominic Foord (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509693/1 | 01/10/2016 | 30/09/2021 | |||
| 1796035 | Studentship | EP/N509693/1 | 01/10/2016 | 31/03/2020 | Dominic Foord |
| Description | We successfully were able to show the birational rigidity of a class of Fano varieties, namely that of cyclic covers containing singular points. A paper has been submitted, and accepted to a journal pending corrections. |
| Exploitation Route | The result is of interest to specialists of algebraic geometry, and specifically those in the field of birational geometry concerned with the birational classification (MMP) of varieties. |
| Sectors | Education |